# the normal approximation

• Oct 22nd 2010, 11:30 AM
terminator
the normal approximation
A clothing manufacturer estimates from past quality control inspections that 4.8% of sweatshirts produced are irregular. If an inspector randomly selects 650 sweatshirts, estimate the probability that at least 30 are irregular.
• Oct 22nd 2010, 01:03 PM
mr fantastic
Quote:

Originally Posted by terminator
A clothing manufacturer estimates from past quality control inspections that 4.8% of sweatshirts produced are irregular. If an inspector randomly selects 650 sweatshirts, estimate the probability that at least 30 are irregular.

Where are you stuck in applying the normal approximation to the binomial distribution? Please show some effort.
• Oct 22nd 2010, 05:22 PM
terminator
np = 350x0.10 = 35
n(1-p) =350 x 0.90 = =315

np>=5, n(1-p) >=5
Therefore, the approximation is resonably close to a normal distribution because
np <= 5 and n(1-p) >=5
Now I can calculate the standard deviation
mean = np =35
sd= sqr(npq) =5.61
How do I calculate the probability?

"In mathematics, you don't understand things. You just get used to them." -- Johann von Neumann
• Oct 22nd 2010, 09:34 PM
mr fantastic
Quote:

Originally Posted by terminator
np = 350x0.10 = 35
n(1-p) =350 x 0.90 = =315

np>=5, n(1-p) >=5
Therefore, the approximation is resonably close to a normal distribution because
np <= 5 and n(1-p) >=5
Now I can calculate the standard deviation
mean = np =35
sd= sqr(npq) =5.61
How do I calculate the probability?

"In mathematics, you don't understand things. You just get used to them." -- Johann von Neumann

http://courses.wcupa.edu/rbove/Beren...section6_5.pdf
• Oct 23rd 2010, 05:09 AM
terminator
Thanks mr.Fantastic - you're a nice man
"In mathematics, you don't understand things. You just get used to them." -- Johann von Neumann